He was reportedly subpoenaed by former FBI director Robert Mueller, who is leading an inquiry into alleged collusion with Russia during the 2016 election campaign.
Mr Bannon appeared separately on Tuesday before a Congressional panel.
Congress is holding its own inquiry into the allegations.
Mr Bannon was subpoenaed last week, the New York Times reports, quoting an unnamed person with direct knowledge of the matter.
However the summons could be a negotiating tactic by Mr Mueller to persuade Mr Bannon to agree to be questioned by investigators in the less formal setting of the special counsel's offices in Washington, the paper's source added.
What is Mr Mueller investigating?
He was appointed by the US justice department in May of last year to oversee an investigation into possible Russian meddling in the 2016 presidential election.
Mr Trump's campaign and transition teams have been accused of colluding with Russian agents to influence the US election in the Republican candidate's favour.
US intelligence agencies, including the CIA and NSA, concluded with "high confidence" in 2016 that Russia was behind an effort to thumb the scale of the US election for Mr Trump.
Both the Russian and US presidents have poured scorn on suggestions of collusion, with Mr Trump calling it "the greatest political witch hunt in history".
Why is Steve Bannon of such interest?
He helped shape Mr Trump's "America First" election campaign message and served as one of his closest aides before being sacked in August.
But he recently fell out with Mr Trump publicly after reportedly making comments about the president and his family in a newly-published book, Fire and Fury, by Michael Wolff.
He was quoted as calling a meeting in June 2016 between Mr Trump's son Donald Jr and a group of Russians "treasonous".
What do we know about that meeting?
It took place at Trump Tower in New York and also involved Mr Trump's son-in-law, Jared Kushner, his then-campaign chairman, Paul Manafort, and an influential Russian lawyer, Natalia Veselnitskaya.
A Russian intermediary had contacted Mr Trump Jr with a promise to provide material that would "incriminate" Democratic presidential candidate Hillary Clinton.
Mr Trump Jr later defended the meeting, saying Ms Veselnitskaya had offered only "inane nonsense" but he also said he "probably would have done things a little differently" in retrospect.
How far has the Mueller inquiry progressed?
Four people have been charged:
- Paul Manafort and Rick Gates, his former business associate, pleaded not guilty to charges of money laundering unrelated to the 2016 election
- George Papadopoulos, a former Trump campaign adviser, admitted lying to the FBI about his contacts with Russians
- Michael Flynn, a former national security adviser to the Trump administration, pleaded guilty to lying to the FBI over meetings he had with Russian ambassador Sergei Kislyak
Why was Mr Bannon in Congress?
The House Intelligence Committee is also investigating the allegations of Russian interference in the 2016 election. Its proceedings on Tuesday were not open to the public.
This is one of four investigations being conducted by Congress into the alleged collusion, with others launched by the Senate Intelligence Committee, the Senate Judiciary Committee and the House Oversight Committee.